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An Efficient Algorithm for Elastic I-optimal Design of Generalized Linear Models

The generalized linear models (GLMs) are widely used in statistical analysis and the related design issues are undoubtedly challenging. The state-of-the-art works mostly apply to design criteria on the estimates of regression coefficients. The prediction accuracy is usually critical in modern decision making and artificial intelligence applications. It is of importance to study optimal designs from the prediction aspects for generalized linear models. In this work, we consider the Elastic I-optimality as a prediction-oriented design criterion for generalized linear models, and develop efficient algorithms for such $\text{EI}$-optimal designs. By investigating theoretical properties for the optimal weights of any set of design points and extending the general equivalence theorem to the $\text{EI}$-optimality for GLMs, the proposed efficient algorithm adequately combines the Fedorov-Wynn algorithm and multiplicative algorithm. It achieves great computational efficiency with guaranteed convergence. Numerical examples are conducted to evaluate the feasibility and computational efficiency of the proposed algorithm.